Is the topic research for a post-doc position supposed to be more general than the research conducted towards a PhD degree? Or rather the opposite?
Getting a Ph.D. is establishing that you are capable of doing a significant piece of research. A postdoc is then your opportunity to start defining the direction in which you are going to take your research, professionally.
As JeffE says, it is usually (though not always) a good idea to be doing something different in your postdoc than you were for your Ph.D. The reason for this is that otherwise you risk getting "stuck" in your little niche and never really moving beyond whatever happened to be your thesis and into the wider worlds of research.
A postdoc, then, is a chance to broaden yourself, to shift your direction (within reasonable bounds), to build momentum in a direction, and generally to start spreading your wings and leaving the nest. How exactly one does that is as varied as are the people who pursue science as their career.